Diffusion coefficients increase

Siemes and Weiss (SI4) investigated axial mixing of the liquid phase in a two-phase bubble-column with no net liquid flow. Column diameter was 42 mm and the height of the liquid layer 1400 mm at zero gas flow. Water and air were the fluid media. The experiments were carried out by the injection of a pulse of electrolyte solution at one position in the bed and measurement of the concentration as a function of time at another position. The mixing phenomenon was treated mathematically as a diffusion process. Diffusion coefficients increased markedly with increasing gas velocity, from about 2 cm2/sec at a superficial gas velocity of 1 cm/sec to from 30 to 70 cm2/sec at a velocity of 7 cm/sec. The diffusion coefficient also varied with bubble size, and thus, because of coalescence, with distance from the gas distributor. 

A high diffusion coefficient increases the rate of diffusion, all else being the same. The diffusion coefficient is determined in part by molecular size and shape. Small molecules tend to have high diffusion coefficients, which is one reason why formaldehyde penetrates faster than glutaraldehyde. In addition, interactions between the chemical and its environment will influence the diffusion coefficient. Thus, if the chemical hydrogen bonds to the water around it, the diffusion coefficient will be lower and the rate of diffusion will be reduced. 

Both the diffusion coefficient and the solubility coefficient vary with temperature in accordance with an Arrhenius relationship. The diffusion coefficient increases with temperature, but the solubility coefficient increases for gases and decreases for vapours. For a full treatment of absorption a text on mass transport should be consulted. 

Molecular dynamics simulations [183] have suggested that the diffusion coefficient increases with increasing ratio in the layers, which can... 

The diffusion coefficient increases rapidly with temperature. The dependence of diffusivity on temperature also follows the Arrhenius relation,... 

This relative invariance of signal may be a consequence of a compensation effect. That is, as temperature increases, the test gas becomes slightly less dense on a moles CO/cm3 basis, but the diffusion coefficient increases slightly. 

Second-Order Moment. The linearity of y U /2L vs. l/t/B2 is shown in Figure 4. From the slope of the straight line, the axial dispersion coefficient D can be calculated. With the assumption that kR = Z)Ab, Da and Di can be calculated from the second and third terms in the bracket of the right-hand side of Equation 6 by varying the particle size. The results are given in Table II. As expected, both inter- and intracrystalline diffusion coefficients increase with temperature. The values obtained for Di in Na mordenite are somewhat smaller than those obtained by Satterfield and Frabetti (7) and Satterfield and Margetts (8) which were obtained at a lower temperature. However, Frabetti reported that diffusion co-... 

The results of the study show that temperature has significant effect on both the partition coefficient and the diffusion coefficient of formaldehyde emissions from the four materials tested. For all four materials, the partition coefficient decreases while the diffusion coefficient increases with increasing temperature. 

Results are shown in Figs. 12 and 13. All blend specimens were set iso-thermally above LCST and kept there for a maximum of 5 min. As will be seen, this corresponds only in some cases to an early stage of spinodal decomposition depending on temperature. The diffusion coefficients governing the dynamics of phase dissolution below LCST are in the order of 10"14 cm2 s"1. Figure 12 reflects the influence of the mobility coefficient on the phase dissolution. As can be seen, the apparent diffusion coefficient increases with increasing temperature of phase dissolution which expresses primarily the temperature dependence of the mobility coefficient. Furthermore, it becomes evident that the mobility obeys an Arrhenius-type equation. Similar results have been reported for phase dis-... 

From this equation it can be seen that the concentration polarization will be smaller with an increased concentration (activity) of ions in the solution at a given current density. Its value can also be decreased by increasing the term k = nDF/T8. This can be achieved either by the application of higher temperature (the diffusion coefficient increases in proportion to the temperature), or by agitating the solution which would reduce the thickness of the diffusion layer. Concentration polarization can be reduced by agitating, but not comple-... 

Wood has been reacted with propylene oxide and mechanical properties determined [25]. Maple specimens were reacted to 20-22 WPG and subjected to standard ASTM tests. The following is a summary of the results comparing propylene oxide-modified specimens to controls. MOE was decreased by 14%, MOR decreased by 17%, fiber stress at proportional limit reduced by 9%, maximum crushing strength decreased by 10%, radial hardness increased by 5%, tangential and longitudinal hardness remained unchanged, and the diffusion coefficient increased by 29%. 

Fig. 7.24 illustrates in four graphs how the optimum linear velocity, optimum d /L. optimum, column length, optimum dimensionless loading, resulting plate count, yield, cycle time, cost per gram (S/g) and production rate (kg/yr) vary with the product diffusivity for a 30 cm ID column. This result allows comparison of the added difficulty of separating proteins and small molecules by looking at the sole etFect of the diffusion coefficient. As the diffusion coefficient increases ... 

Band broadening and temperature The five terms of Equation (24-14) can be examined in the context of the influence of temperature on flow rates, retention volumes, and diffusion coefficients to obtain an estimate of the overall influence of temperature on band broadening. Through thermal expansion, temperature also influences such factors as thickness of a liquid film and particle and column diameters, and it may also influence slightly the empirical constants in (24-14). With a liquid mobile phase, flow velocity (with the same inlet and outlet pressures) is strongly dependent on temperature. But with flow velocity u maintained constant the first term of (24-14) becomes smaller as diffusion coefficients increase in the mobile phase. For flow rates near the optimum the first term is approximately inversely proportional to The second and third terms increase in direct proportion to the diffusion coefficients in the mobile and stationary phases D and D, whereas the fourth and fifth... 

Diffusion coefficients increase with temperature. The diffusion coefilcieni (and thus the mass diffusion rate) of carbon through iron during a hardening process, for example, increa.scs by 6000 limes as the temperature is raised rrom500°C to 1000°C. 

Xiao et al [37] included interaction between molecules in the diffusion coefficient by allowing each site to be occupied by a maximum of two molecules. If molecules are on the same site, they interact with each other. The diffusion coefficient increases with increasing interaction between molecules. The apparent diffusivity becomes... 

As shown by Zawodzinski et al., the dramatic uptake of water upon preswelling the membrane in glycerol at elevated temperatures (Fig. 27) substantially affects the transport properties in the membrane. In Table 8, the H intradiffusion coefficient is given for several different water contents. The water self-diffusion coefficient increases to 1.7 x 10 cm /s as the water content reaches the exceptionally high level of A = 80 (liquid water has a self-diffusion coefficient of 2.2 x cm /s at the same temperature). 

As discussed in the last section, Eqs. (15) and (16) suggest that the solubility of solid solutes increases with increasing temperature. Furthermore, the diffusion coefficient increases with increasing temperature, and this is expected to enhance the dissolution rate. In some cases, however, secondary considerations, such as reactions of the solute, can place a limit on the operation temperature. 

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